// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include "svd_fill.h"
#include <Eigen/Eigenvalues>
#include <Eigen/SparseCore>
#include <limits>

template<typename MatrixType>
void
selfadjointeigensolver_essential_check(const MatrixType& m)
{
	typedef typename MatrixType::Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;
	RealScalar eival_eps =
		numext::mini<RealScalar>(test_precision<RealScalar>(), NumTraits<Scalar>::dummy_precision() * 20000);

	SelfAdjointEigenSolver<MatrixType> eiSymm(m);
	VERIFY_IS_EQUAL(eiSymm.info(), Success);

	RealScalar scaling = m.cwiseAbs().maxCoeff();

	if (scaling < (std::numeric_limits<RealScalar>::min)()) {
		VERIFY(eiSymm.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
	} else {
		VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiSymm.eigenvectors()) / scaling,
						 (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal()) / scaling);
	}
	VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
	VERIFY_IS_UNITARY(eiSymm.eigenvectors());

	if (m.cols() <= 4) {
		SelfAdjointEigenSolver<MatrixType> eiDirect;
		eiDirect.computeDirect(m);
		VERIFY_IS_EQUAL(eiDirect.info(), Success);
		if (!eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps)) {
			std::cerr << "reference eigenvalues: " << eiSymm.eigenvalues().transpose() << "\n"
					  << "obtained eigenvalues:  " << eiDirect.eigenvalues().transpose() << "\n"
					  << "diff:                  " << (eiSymm.eigenvalues() - eiDirect.eigenvalues()).transpose()
					  << "\n"
					  << "error (eps):           "
					  << (eiSymm.eigenvalues() - eiDirect.eigenvalues()).norm() / eiSymm.eigenvalues().norm() << "  ("
					  << eival_eps << ")\n";
		}
		if (scaling < (std::numeric_limits<RealScalar>::min)()) {
			VERIFY(eiDirect.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
		} else {
			VERIFY_IS_APPROX(eiSymm.eigenvalues() / scaling, eiDirect.eigenvalues() / scaling);
			VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiDirect.eigenvectors()) / scaling,
							 (eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal()) / scaling);
			VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues() / scaling,
							 eiDirect.eigenvalues() / scaling);
		}

		VERIFY_IS_UNITARY(eiDirect.eigenvectors());
	}
}

template<typename MatrixType>
void
selfadjointeigensolver(const MatrixType& m)
{
	/* this test covers the following files:
	   EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
	*/
	Index rows = m.rows();
	Index cols = m.cols();

	typedef typename MatrixType::Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;

	RealScalar largerEps = 10 * test_precision<RealScalar>();

	MatrixType a = MatrixType::Random(rows, cols);
	MatrixType a1 = MatrixType::Random(rows, cols);
	MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
	MatrixType symmC = symmA;

	svd_fill_random(symmA, Symmetric);

	symmA.template triangularView<StrictlyUpper>().setZero();
	symmC.template triangularView<StrictlyUpper>().setZero();

	MatrixType b = MatrixType::Random(rows, cols);
	MatrixType b1 = MatrixType::Random(rows, cols);
	MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
	symmB.template triangularView<StrictlyUpper>().setZero();

	CALL_SUBTEST(selfadjointeigensolver_essential_check(symmA));

	SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
	// generalized eigen pb
	GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);

	SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
	VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
	VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());

	// generalized eigen problem Ax = lBx
	eiSymmGen.compute(symmC, symmB, Ax_lBx);
	VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
	VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())
			   .isApprox(symmB.template selfadjointView<Lower>() *
							 (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()),
						 largerEps));

	// generalized eigen problem BAx = lx
	eiSymmGen.compute(symmC, symmB, BAx_lx);
	VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
	VERIFY(
		(symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()))
			.isApprox((eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));

	// generalized eigen problem ABx = lx
	eiSymmGen.compute(symmC, symmB, ABx_lx);
	VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
	VERIFY(
		(symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()))
			.isApprox((eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));

	eiSymm.compute(symmC);
	MatrixType sqrtSymmA = eiSymm.operatorSqrt();
	VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA * sqrtSymmA);
	VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>() * eiSymm.operatorInverseSqrt());

	MatrixType id = MatrixType::Identity(rows, cols);
	VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));

	SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
	VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
	VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
	VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
	VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
	VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());

	eiSymmUninitialized.compute(symmA, false);
	VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
	VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
	VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());

	// test Tridiagonalization's methods
	Tridiagonalization<MatrixType> tridiag(symmC);
	VERIFY_IS_APPROX(tridiag.diagonal(), tridiag.matrixT().diagonal());
	VERIFY_IS_APPROX(tridiag.subDiagonal(), tridiag.matrixT().template diagonal<-1>());
	Matrix<RealScalar, Dynamic, Dynamic> T = tridiag.matrixT();
	if (rows > 1 && cols > 1) {
		// FIXME check that upper and lower part are 0:
		// VERIFY(T.topRightCorner(rows-2, cols-2).template triangularView<Upper>().isZero());
	}
	VERIFY_IS_APPROX(tridiag.diagonal(), T.diagonal());
	VERIFY_IS_APPROX(tridiag.subDiagonal(), T.template diagonal<1>());
	VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()),
					 tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
	VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()),
					 tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint());

	// Test computation of eigenvalues from tridiagonal matrix
	if (rows > 1) {
		SelfAdjointEigenSolver<MatrixType> eiSymmTridiag;
		eiSymmTridiag.computeFromTridiagonal(
			tridiag.matrixT().diagonal(), tridiag.matrixT().diagonal(-1), ComputeEigenvectors);
		VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmTridiag.eigenvalues());
		VERIFY_IS_APPROX(tridiag.matrixT(),
						 eiSymmTridiag.eigenvectors().real() * eiSymmTridiag.eigenvalues().asDiagonal() *
							 eiSymmTridiag.eigenvectors().real().transpose());
	}

	if (rows > 1 && rows < 20) {
		// Test matrix with NaN
		symmC(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
		SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
		VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
	}

	// regression test for bug 1098
	{
		SelfAdjointEigenSolver<MatrixType> eig(a.adjoint() * a);
		eig.compute(a.adjoint() * a);
	}

	// regression test for bug 478
	{
		a.setZero();
		SelfAdjointEigenSolver<MatrixType> ei3(a);
		VERIFY_IS_EQUAL(ei3.info(), Success);
		VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(), RealScalar(1));
		VERIFY((ei3.eigenvectors().transpose() * ei3.eigenvectors().transpose()).eval().isIdentity());
	}
}

template<int>
void
bug_854()
{
	Matrix3d m;
	m << 850.961, 51.966, 0, 51.966, 254.841, 0, 0, 0, 0;
	selfadjointeigensolver_essential_check(m);
}

template<int>
void
bug_1014()
{
	Matrix3d m;
	m << 0.11111111111111114658, 0, 0, 0, 0.11111111111111109107, 0, 0, 0, 0.11111111111111107719;
	selfadjointeigensolver_essential_check(m);
}

template<int>
void
bug_1225()
{
	Matrix3d m1, m2;
	m1.setRandom();
	m1 = m1 * m1.transpose();
	m2 = m1.triangularView<Upper>();
	SelfAdjointEigenSolver<Matrix3d> eig1(m1);
	SelfAdjointEigenSolver<Matrix3d> eig2(m2.selfadjointView<Upper>());
	VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());
}

template<int>
void
bug_1204()
{
	SparseMatrix<double> A(2, 2);
	A.setIdentity();
	SelfAdjointEigenSolver<Eigen::SparseMatrix<double>> eig(A);
}

EIGEN_DECLARE_TEST(eigensolver_selfadjoint)
{
	int s = 0;
	for (int i = 0; i < g_repeat; i++) {

		// trivial test for 1x1 matrices:
		CALL_SUBTEST_1(selfadjointeigensolver(Matrix<float, 1, 1>()));
		CALL_SUBTEST_1(selfadjointeigensolver(Matrix<double, 1, 1>()));
		CALL_SUBTEST_1(selfadjointeigensolver(Matrix<std::complex<double>, 1, 1>()));

		// very important to test 3x3 and 2x2 matrices since we provide special paths for them
		CALL_SUBTEST_12(selfadjointeigensolver(Matrix2f()));
		CALL_SUBTEST_12(selfadjointeigensolver(Matrix2d()));
		CALL_SUBTEST_12(selfadjointeigensolver(Matrix2cd()));
		CALL_SUBTEST_13(selfadjointeigensolver(Matrix3f()));
		CALL_SUBTEST_13(selfadjointeigensolver(Matrix3d()));
		CALL_SUBTEST_13(selfadjointeigensolver(Matrix3cd()));
		CALL_SUBTEST_2(selfadjointeigensolver(Matrix4d()));
		CALL_SUBTEST_2(selfadjointeigensolver(Matrix4cd()));

		s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
		CALL_SUBTEST_3(selfadjointeigensolver(MatrixXf(s, s)));
		CALL_SUBTEST_4(selfadjointeigensolver(MatrixXd(s, s)));
		CALL_SUBTEST_5(selfadjointeigensolver(MatrixXcd(s, s)));
		CALL_SUBTEST_9(selfadjointeigensolver(Matrix<std::complex<double>, Dynamic, Dynamic, RowMajor>(s, s)));
		TEST_SET_BUT_UNUSED_VARIABLE(s)

		// some trivial but implementation-wise tricky cases
		CALL_SUBTEST_4(selfadjointeigensolver(MatrixXd(1, 1)));
		CALL_SUBTEST_4(selfadjointeigensolver(MatrixXd(2, 2)));
		CALL_SUBTEST_5(selfadjointeigensolver(MatrixXcd(1, 1)));
		CALL_SUBTEST_5(selfadjointeigensolver(MatrixXcd(2, 2)));
		CALL_SUBTEST_6(selfadjointeigensolver(Matrix<double, 1, 1>()));
		CALL_SUBTEST_7(selfadjointeigensolver(Matrix<double, 2, 2>()));
	}

	CALL_SUBTEST_13(bug_854<0>());
	CALL_SUBTEST_13(bug_1014<0>());
	CALL_SUBTEST_13(bug_1204<0>());
	CALL_SUBTEST_13(bug_1225<0>());

	// Test problem size constructors
	s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
	CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s));
	CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s));

	TEST_SET_BUT_UNUSED_VARIABLE(s)
}
